Have you ever bought a bunch of celery and find that the bottom couple of inches is more "core" than stem?
This happened every so often, when I buy a bundle of celery. The first few stalks peel off nicely. Then the stalks grow shorter and shorter, as this core in the bottom of the bundle develops. That core may not be useful for celery sticks, but it can be used in soups and stews.
I simply chop off the core, cut off the very bottom, wash and chop fine.
It gives flavor and texture to my soups and stews.